It has been recognized that certain media having a polarization susceptability provide sensitive ways of manipulating beams of incident electromagnetic radiation. Such media are said to possess nonlinear polarization. The size of the effects attributable to such nonlinear polarization depends on the arrangement of electrically charged particles (electrons, ions and nuclei) within the media. To obtain the highest nonlinear polarization property of a medium, the molecules within the medium must be arranged so that the nonlinear properties of the individual polar molecules within the medium do not cancel each other out.
The nonlinear optical response of a molecule can be described in the dipole approximation by the following expression: EQU .mu.=.mu..sub.0 +.alpha..multidot.E+.beta..multidot..multidot.EE+.gamma..multidot..multido t..multidot.EEE+. . . ,
where .mu. is the total dipole moment which consists of the sum of .mu..sub.0, the permanent moment, and the induced moment in the molecule; .alpha. is the linear polarizability tensor, and .beta. and .gamma. are the second- and third-order nonlinear polarizability or hyperpolarizability tensors; .alpha., .beta. and .gamma. quantify the moment induced by E, the local electric field.
To describe an ensemble of molecules, such as a crystal, the macroscopic constitutive relationship should be used: EQU P=P.sub.0 +.chi..sup.(1) .multidot.E+.chi..sup.(2) .multidot..multidot.EE+.chi..sup.(3) .multidot..multidot..multidot.EEE+. . . ,
where P is the total polarization density which similarly consists of the sum of P.sub.0, the permanent polarization density, and the induced polarization density; .chi..sup.(1) is the linear susceptibility tensor, and .chi..sup.(2) and .chi..sup.(3) are the second- and third-order nonlinear susceptibility tensors; E is the Maxwellian electric field. Second-order nonlinear optical phenomena such as second harmonic generation, sum and difference frequency mixing, parametric processes and electro-optical effects arise, by definition, from the presence of the .chi..sup.(2) term.
Franken, et al., Phys. Rev. Lett., Vol. 7, 118-119 (1961), disclose the observation of second harmonic generation upon the passage of a pulsed ruby laser beam through crystalline quartz. They observed the generation of the second harmonic of light, in which light of 694.3 nm wavelength was converted to light of 347.2 nm wavelength. The use of a laser beam remains the only practical way to generate an E large enough to be able to detect the SHG phenomena.
To have a large .chi..sup.(2), the ensemble should contain molecules possessing large elements in their .beta. tensors and these molecules must be oriented in a fashion which prevents extensive mutual cancellation of their second-order nonlinear polarizability. The extent of cancellation depends on details of molecular alignment. For example, in centrosymmetric crystals this cancellation is complete. Thus it is widely known that to obtain nonvanishing .chi..sup.(2) noncentrosymmetric structures are required. Approximate theory of local-field behavior allows the calculation of the projection of molecular nonlinear polarizability, .beta., to the macroscopic scale based largely on details of molecular orientation. An important result is that for each crystal class there are optimal tilts of the constituent molecules relative to the crystal axes which maximize various elements of the .chi..sup.(2) tensor. Useful reviews of the art relating to nonlinear properties of organic materials are given in the following references: "Nonlinear Optical Properties of Organic and Polymeric Materials", D. J. Williams, ed., American Chemical Society, Washington, D.C. (1983); D. J. Williams, Angew. Chem., Int. Ed. Engl., Vol. 23, 690 (1984); "Nonlinear Optical Properties of Organic Molecules and Crystals", Vol. 1 and 2, D. S. Chemla et al., ed., Academic Press, New York, NY (1987).
Although a large number of organic and inorganic materials capable of SHG have been found since Franken's discovery, an intense search continues. Through many years of research, it is now known that an organic molecule having a conjugated x electron system or a low-lying charge transfer excited state often has a large second-order polarizability. Many molecules with large .beta. elements have been discovered based on these principles. However, crystals of many of these molecules have no practical use for second-order nonlinear optical effects because of their small .chi..sup.(2) elements. The failure to efficiently project second-order nonlinearity from the molecular to the macroscopic level results from unfavorable alignment of molecules in the structure of the crystals they form. At present the prediction of crystal structures is not a reliable science. Thus the empirical determination of second-order nonlinearity is a key step in the identification of new materials for these applications.
It is an object of the present invention to provide optical elements useful in second harmonic generation. It is a further object of the present invention to provide optical devices, electro-optic modulators and the like incorporating these optical elements. A feature of the present invention is the use of noncentrosymmetric crystalline organic compounds for the optical elements. It is an advantage of the present invention to provide noncentrosymmetric crystalline organic compounds suitable for containment within polymeric binders, glass and the like. These and other objects, features and advantages will become apparent upon bearing reference to the following description of the invention.